The magnitude, or size, of a vector
a\underline{i}+b\underline{j} in 2 dimensions is
found by the formula: \sqrt{(a^2+b^2)}

The magnitude, or size, of a vector a\underline{i}+b\underline{j}+c\underline{k} in 3 dimensions is found by the formula: \sqrt{(a^2+b^2+c^2)}

The magnitude, or size, of a vector a\underline{i}+b\underline{j}+c\underline{k} in 3 dimensions is found by the formula: \sqrt{(a^2+b^2+c^2)}

## Summary/Background

The formula for the magnitude of a vector is basically Pythagoras' theorem extended to 3 dimensions.

## Software/Applets used on this page

## Glossary

### magnitude

A measure of the size of a mathematical object

### union

The union of two sets A and B is the set containing all the elements of A and B.

### vector

A mathematical object with magnitude and direction.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra |

AQA A2 Maths 2017 | Mechanics | Kinematics | 3D Vectors |

AQA AS Maths 2017 | Mechanics | Vectors | Vector Basics |

AQA AS/A2 Maths 2017 | Mechanics | Vectors | Vector Basics |

CBSE XII (India) | Vectors and 3-D Geometry | Vectors | Types, equal, unit, parallel, collinear |

CCEA A-Level (NI) | C4 | Vectors | Vector algebra |

CIE A-Level (UK) | P1 | Vectors | Vector algebra |

J Vectors | J3 Basic Operations and Diagrams | Vector Algebra | |

Edexcel A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra |

Edexcel A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors |

Edexcel AS Maths 2017 | Pure Maths | Vectors | Vector Basics |

Edexcel AS/A2 Maths 2017 | Pure Maths | Vectors | Vector Basics |

I.B. Higher Level | 4 | Vectors | Vector algebra |

I.B. Standard Level | 4 | Vectors | Vector algebra |

Methods (UK) | M4 | Vectors | Vector algebra |

OCR A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra |

OCR A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors |

OCR AS Maths 2017 | Pure Maths | Vectors | Vector Basics |

OCR MEI A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors |

OCR MEI AS Maths 2017 | Pure Maths | Vectors | Vector Basics |

OCR-MEI A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra |

Pre-Calculus (US) | E1 | Vectors | Vector algebra |

Pre-U A-Level (UK) | 6 | Vectors | Vector algebra |

Scottish (Highers + Advanced) | HM3 | Vectors | Vector algebra |

Scottish Highers | M3 | Vectors | Vector algebra |

Universal (all site questions) | V | Vectors | Vector algebra |

WJEC A-Level (Wales) | C4 | Vectors | Vector algebra |